Journal of Symbolic Logic

On Polish groups admitting a compatible complete left-invariant metric

Maciej Malicki

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Abstract

We prove that the set of all Polish groups admitting a compatible complete left-invariant metric (called CLI) is coanalytic non-Borel as a subset of a standard Borel space of all Polish groups. As an application of this result, we show that there does not exist a weakly universal CLI group. This, in particular, answers in the negative a question of H.Becker.

Article information

Source
J. Symbolic Logic, Volume 76, Issue 2 (2011), 437-447.

Dates
First available in Project Euclid: 19 May 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1305810757

Digital Object Identifier
doi:10.2178/jsl/1305810757

Mathematical Reviews number (MathSciNet)
MR2830410

Zentralblatt MATH identifier
1221.03045

Citation

Malicki, Maciej. On Polish groups admitting a compatible complete left-invariant metric. J. Symbolic Logic 76 (2011), no. 2, 437--447. doi:10.2178/jsl/1305810757. https://projecteuclid.org/euclid.jsl/1305810757


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